USCG Captain's License Exam Guide

Cargo Handling and Vessel Stability

Vessel stability and cargo handling appear on every USCG OUPV and Master license exam. This guide covers every tested concept: the stability triangle (G, B, M), metacentric height, the GZ righting arm curve, free surface effect, angle of loll, weight shifts, trim calculations, draft mark reading, cargo securing, IMDG dangerous goods classifications, grain stability, and IMO intact stability criteria. Work through each section and you will be ready for every stability and cargo question on exam day.

1. Stability Fundamentals — G, B, and M

Vessel stability is the tendency of a vessel to return to its upright position after being heeled by an external force. Understanding stability requires knowing three key points and how they interact when the vessel is heeled.

K
Keel
Lowest reference point of the hull. All vertical measurements are taken upward from K.
G
Center of Gravity
The point through which the total weight of the vessel acts downward. G moves when weights are shifted, added, or removed.
B
Center of Buoyancy
The geometric center of the underwater volume. B moves as the vessel heels — always shifting toward the low side.
M
Metacenter
The point where a vertical line through the shifted B (when heeled) crosses the vessel centerline. M is fixed for small angles of heel.
GM
Metacentric Height
Vertical distance from G to M. Positive GM = stable. Negative GM = unstable (loll or capsize).
GZ
Righting Arm
Horizontal distance between the line of action of buoyancy and the line of action of gravity when the vessel is heeled. GZ > 0 means righting moment exists.
KB
Height of B above Keel
Approximately 0.53 x draft for a box-shaped hull. Read from hydrostatic tables for actual hull forms.
BM
Metacentric Radius
Distance from B to M. Formula: BM = I / V, where I = second moment of waterplane area and V = displacement volume.
KG
Height of G above Keel
Calculated from the lightship KG plus the moments of all weights added. This is the key variable the master controls through loading decisions.
KM
Height of M above Keel
KM = KB + BM. Read directly from hydrostatic tables for a given displacement. KM = KG + GM, so GM = KM - KG.

The Stability Sequence When Heeled

  1. 1.The vessel heels. G does not move — it stays at the same point in the vessel because no weights have shifted.
  2. 2.The underwater volume changes shape. B shifts toward the low side (more volume is submerged on the low side).
  3. 3.A vertical line drawn upward through the new B position intersects the vessel's centerline at M (the metacenter).
  4. 4.If M is above G (positive GM), the buoyancy force acts through a point higher than the gravity force — a righting moment exists.
  5. 5.The horizontal distance between the lines of action of buoyancy and gravity is called GZ — the righting arm. GZ x displacement = righting moment.

The GM Formula

GM = KB + BM - KG
equivalently: GM = KM - KG (since KM = KB + BM)

KB and BM come from hydrostatic tables (read from the stability booklet at the vessel's current displacement). KG is calculated by the master using the vessel's lightship KG plus the moments of all weights loaded. On the exam, you are typically given KM (read from the table) and asked to find KG or GM.

Exam Example — GM Calculation
Given: Vessel displacement = 800 tons. From stability booklet: KM = 4.2 m. Calculated KG = 3.9 m.
GM = KM - KG = 4.2 - 3.9 = 0.30 m (positive — vessel is stable)
This small positive GM (0.30 m) indicates a tender vessel. The vessel meets minimum stability requirements but will have a slow, rolling motion. Any increase in KG (e.g., adding high cargo) without a corresponding increase in KM could push GM negative.

2. Metacentric Height (GM)

GM is the single most important stability parameter in day-to-day operation. It is the master's primary tool for assessing whether the vessel is safe to sail. The USCG exam tests GM extensively — both conceptually and through calculations.

Large Positive GM
Roll: Short, stiff, snappy — vessel rights quickly
Safety: High resistance to capsize
Problem: Uncomfortable motion; cargo stress; structural fatigue
Called: Stiff vessel
Moderate Positive GM
Roll: Comfortable period — vessel rolls slowly and returns smoothly
Safety: Meets regulatory minima
Problem: Must be monitored during loading and fuel consumption
Called: Well-trimmed vessel
Zero or Negative GM
Roll: Very slow or no return to upright
Safety: Vessel is unstable — loll or capsize risk
Problem: Do not sail without corrective action
Called: Tender vessel (if small positive) / loll (if zero/negative)

Factors That Raise G (Reduce GM)

  • Loading cargo high in the vessel (on deck, in high holds)
  • Consuming ballast from double-bottom tanks (removes low weight)
  • Free surface effect in partially filled tanks (virtual rise in G)
  • Icing on superstructure, rigging, or deck cargo
  • Adding topside weights (radar masts, electronic equipment, passengers on upper decks)
  • Removing low ballast or shifting ballast from low to high tanks

Factors That Lower G (Increase GM)

  • Loading ballast in double-bottom tanks
  • Shifting cargo from high locations to lower holds
  • Removing high cargo or deck cargo
  • Filling tanks that were partially full (eliminating free surface)
  • Discharging cargo from upper decks
Key Exam Rule

The only way to change KM is to change displacement (change the draft). KM comes from the hull form. You cannot change the hull. But you CAN change KG by managing where weights are placed. The master's entire stability job is managing KG relative to KM to keep GM positive and adequate.

3. The GZ Righting Arm Curve

The GZ curve (also called the static stability curve or righting arm curve) plots the righting arm (GZ) in meters against the angle of heel in degrees. It is the most complete picture of a vessel's stability across its full range of motion. Every licensed officer must be able to read and interpret a GZ curve — the USCG exam tests this directly.

Reading the GZ Curve — Key Points

Initial Slope (0° to ~15°)

The slope of the GZ curve near zero equals GM / (57.3 degrees, the radian conversion). A steep initial slope means large positive GM and a stiff vessel. The tangent to the curve at 0° is proportional to GM — examiners use this to ask whether GM increased or decreased based on a modified curve.

Angle of Maximum GZ

The heel angle at which the righting arm reaches its peak value. Typically 30°–45° for well-designed vessels. IMO criteria require the maximum GZ to occur at an angle not less than 25°. Beyond this angle, the righting arm decreases — the vessel is losing its ability to self-right.

Area Under the Curve (Dynamic Stability)

The area under the GZ curve between two angles represents the energy the vessel can absorb from waves and wind without capsizing. IMO requires the area under the GZ curve from 0° to 30° to be not less than 0.055 meter-radians, and from 0° to 40° (or the flooding angle if less) to be not less than 0.090 meter-radians. The area between 30° and 40° must not be less than 0.030 meter-radians.

Angle of Vanishing Stability (AVS)

The angle where GZ returns to zero on the descending side of the curve. Beyond the AVS, the vessel has negative righting moment and will capsize. A typical AVS for a well-designed vessel is 70°–120°. Vessels with AVS below 60° are considered to have limited range of stability. The exam may show two GZ curves and ask which vessel is safer in heavy weather — the one with the greater AVS and larger area under the curve.

Effect of Increased KG on the GZ Curve

Raising G (increasing KG) shifts the entire GZ curve downward. The initial slope decreases (less GM), the peak GZ value decreases, and the AVS decreases. If KG rises high enough, the initial GZ value goes negative — the vessel is now in the loll condition. This is why even a small increase in G from free surface effect can be critical on a vessel already operating with low positive GM.

IMO Intact Stability Criteria — Summary Table
CriterionMinimum Value
Area under GZ curve, 0° to 30°≥ 0.055 m·rad
Area under GZ curve, 0° to 40° (or flooding angle)≥ 0.090 m·rad
Area under GZ curve, 30° to 40°≥ 0.030 m·rad
Maximum GZ value≥ 0.20 m at angle ≥ 25°
Initial GM (corrected for free surface)≥ 0.15 m
Angle of maximum GZ≥ 25°

4. Positive, Negative, and Neutral Stability

Positive Stability

M is above G. When heeled, the buoyant force (acting upward through B) and the gravitational force (acting downward through G) form a couple that tends to return the vessel to upright. GZ is positive at all angles up to the AVS.

Condition: GM positive
GZ curve: Starts at zero, rises positive, returns to zero at AVS
Action needed: None — vessel is safe

Neutral Stability

M coincides exactly with G. GM equals zero. When heeled, the vessel stays at that angle — no righting moment and no capsizing moment. In practice, neutral stability is an unstable boundary condition that a vessel passes through on the way to negative stability.

Condition: GM = 0
GZ curve: Flat line at GZ = 0
Action needed: Immediate corrective action required

Negative Stability

G is above M. GM is negative. When heeled even slightly, the vessel tends to heel further rather than return to upright. The vessel will settle at the angle of loll (where GZ momentarily equals zero again due to the rising B) or capsize if the heeling force exceeds the range of positive GZ.

Condition: GM negative
GZ curve: Starts negative, may become positive at larger angles (loll)
Action needed: Do not sail — correct immediately
Critical Exam Point — Righting Moment Formula
Righting Moment = GZ x Displacement

The righting moment is in foot-tons or meter-tons. GZ is in feet or meters; displacement is in long tons or metric tons. A heavier vessel with the same GZ has a greater righting moment and is harder to capsize. A lighter vessel (in ballast, after cargo discharge) has less righting moment for the same GZ — this is why vessels in ballast condition are often more tender than vessels fully loaded.

5. List vs. Angle of Loll

This is one of the most heavily tested distinctions on the USCG exam. List and loll look similar from the outside (vessel heeling to one side) but have completely different causes and require opposite corrective actions. Applying the wrong correction to loll can sink the vessel.

List

Cause: Transverse center of gravity (TCG) is off the centerline. G has moved to one side due to asymmetric loading — cargo loaded on one side only, fuel consumed from one tank only, or ballast in one wing tank only.
GM: Positive. The vessel is stable but heeled. The GZ curve is shifted — the vessel's equilibrium angle is not zero but the angle of list. The vessel will resist further heeling beyond the list angle.
Behavior: Vessel consistently heels to the same side. Does not switch sides. Roll is still present but centered on the list angle rather than upright.
Correction: Move weight back to the centerline or to the high side. Transfer ballast from the low wing tank to the high side. Discharge cargo from the low side or load cargo on the high side.

Angle of Loll

Cause: Negative GM. G has risen above M due to high loading, excessive free surface effect, heavy icing, or other factors that raised G. The vessel has no initial righting moment when upright.
GM: Negative (at the upright position). The GZ curve starts below zero, meaning the vessel is pushed away from upright rather than toward it. At the loll angle, the rising buoyancy force catches up and GZ = 0 again briefly.
Behavior: Vessel heels to one side (seemingly random — whichever side a small external force tips it). In a seaway, the vessel may switch sides suddenly and violently as wave action lifts B. This sudden switching is a dangerous warning sign.
WRONG correction: Moving weight to the high side temporarily reduces the loll angle — but if the vessel passes through upright (while GM is still negative), it can suddenly lurch to the other side and capsize.
CORRECT correction: Lower G. Add ballast to the double-bottom tanks. Remove high-weight cargo. Fill slack tanks (reduces free surface effect). Do NOT move weight to the high side as the first action.
How to Distinguish List from Loll on the Exam
Clue 1 — Loading history: If the question describes asymmetric loading (cargo on one side, one fuel tank), it is probably list.
Clue 2 — Behavior: If the vessel switches sides or the rolling is sluggish and slow, it is probably loll.
Clue 3 — Prior loading: If the question says cargo was loaded high or tanks are half full, the free surface effect raising G is the mechanism — this is loll.
Clue 4 — GM sign: If GM is stated as negative, the condition is loll regardless of which side the vessel heels to.

6. Free Surface Effect and FSC Calculation

Free surface effect (FSE) is the loss of metacentric height caused by liquid sloshing in a partially filled tank or compartment. It is one of the leading causes of vessel capsizing and one of the most tested topics on the USCG exam. Understanding why it occurs and how to minimize it is essential.

Why Free Surface Reduces Stability

When a vessel heels, liquid in a slack tank shifts to the low side. This shifts the center of gravity of that liquid toward the low side, pulling the ship's overall G to the low side and upward. The result is a virtual rise in G — as if G had physically moved up, even though the weight of the liquid has not changed. This virtual rise in G reduces GM.

Free Surface Correction Formula
FSC = (i × ρ_liquid) / (V × ρ_seawater)
— or in simplified practice exam form —
GM_corrected = GM_solid − FSC
i = second moment of area (moment of inertia) of the free surface about its centerline (m⁴ or ft⁴)
V = displacement volume of the vessel (m³ or ft³)
ρ_liquid = density of the liquid in the tank
ρ_seawater = density of seawater (1.025 t/m³)

Key Facts About Free Surface Effect

Width is the dominant factor. The second moment of area (i) is proportional to the CUBE of tank width (i = l × b³ / 12 for a rectangular tank). Doubling the tank width increases FSC by a factor of 8. Wide tanks have dramatically worse free surface effect than narrow tanks of the same capacity.
Fill level matters less than width. A wide tank at 50% fill has far more free surface effect than a narrow tank at 50%. The fill percentage affects the FSC, but width is the primary concern.
Longitudinal subdivisions dramatically help.Installing a centerline baffle or longitudinal bulkhead in a tank divides width by 2. Since i uses b³, this reduces FSC by a factor of 8 for each half. This is why double-bottom tanks on larger vessels have centerline divisions.
Full or empty tanks have zero FSC. A completely full tank has no free surface — the liquid cannot shift. An empty tank has no liquid. The practical rule: keep tanks full or empty; never leave them slack in rough conditions.
Dense liquids have greater FSC. The FSC formula includes the ratio of liquid density to seawater density. Fuel oil (0.85 t/m³) has less FSC than the equivalent volume of saltwater ballast (1.025 t/m³). This is counterintuitive — denser cargo in the same tank creates more FSC.
Exam Calculation Example — FSC
A vessel has GM (solid) = 0.45 m. It has three slack tanks with FSC values (from the stability booklet) of 0.08 m, 0.12 m, and 0.06 m.
Total FSC = 0.08 + 0.12 + 0.06 = 0.26 m
GM (corrected) = 0.45 - 0.26 = 0.19 m
The corrected GM is 0.19 m — above the IMO minimum of 0.15 m but critically low. If any additional weight is added at height, or if another tank goes slack, the vessel may approach negative GM. The master should fill or empty the slack tanks immediately.

7. Stiff vs. Tender Vessels

The terms stiff and tender describe a vessel's roll behavior and are directly related to GM. The exam tests both the definitions and the practical implications for safety and cargo.

Stiff Vessel — Large GM

Roll period: Short (rapid roll)
Roll angle: Small amplitude per wave
Feel: Snappy, violent, uncomfortable
Cargo risk: High acceleration forces — can break lashings, damage fragile cargo, cause cargo to shift
Structural risk: High dynamic stresses on hull, superstructure, masts
Capsize risk: Low
Typical cause: Very low KG — heavy ballast in double bottoms, light superstructure, low cargo
Roll period formula: T = C × B / √GM (shorter T = larger GM)

Tender Vessel — Small GM

Roll period: Long (slow roll)
Roll angle: Large amplitude per wave
Feel: Slow, wallowing, sluggish recovery
Cargo risk: Cargo can shift due to large roll angles; containers can rack
Structural risk: Lower dynamic stresses but higher chance of progressive heel leading to flooding
Capsize risk: Higher — especially if stability criteria are marginal
Typical cause: High KG — heavy deck cargo, high superstructure, topped-off high tanks, free surface effect
Warning sign: Slow return to upright after heeling — vessel hesitates at roll apex
Roll Period and GM — The Practical Test

A master can estimate GM from the natural roll period without a stability calculation. Time the vessel's natural roll period (T) in seconds with a stopwatch. A short, rapid roll period indicates large GM (stiff). A long, slow period indicates small GM (tender). If the period is very long and the vessel hesitates before returning from each roll, the GM may be dangerously small or approaching zero.

T ≈ 0.8 × B / √GM (where B = beam in meters, T = period in seconds, GM in meters)

8. Weight Shifts — Transverse, Longitudinal, Vertical

Shifting a weight already on board does not change displacement or draft. It changes only the position of G. Understanding how G moves in response to weight shifts is fundamental to stability and is heavily tested.

G Moves Toward the Shifted Weight

When a weight is moved from position A to position B, G moves from its original position toward B, along the line connecting the old and new positions of the weight. The formula for the shift of G is:

GG' = (w × d) / W
where w = weight shifted, d = distance shifted, W = total displacement
Direction of ShiftEffect on GEffect on GMEffect on Trim/List
Weight Shifted UpwardG rises — GM decreases — stability reducedNo trim changeNo list change if on centerline
Weight Shifted DownwardG lowers — GM increases — stability improvedNo trim changeNo list change if on centerline
Weight Shifted to StarboardG moves to starboard — TCG off centerlineNo trim changeVessel lists to starboard
Weight Shifted ForwardG moves forward — LCG changesTrim by the head increasesNo list change
Weight Shifted AftG moves aft — LCG changesTrim by the stern increasesNo list change

Transverse Center of Gravity (TCG) and List

The transverse center of gravity (TCG) is G's horizontal distance from the vessel's centerline. A vessel with TCG = 0 has no list (G is on the centerline). Any transverse shift of G produces list. The angle of list can be calculated for small angles as:

tan(θ) = TCG / GM
θ = angle of list; TCG = transverse shift of G from centerline; GM = metacentric height
Exam Example — Transverse Weight Shift
A 500-ton vessel (GM = 0.60 m) shifts 10 tons of cargo 4 meters to starboard.
TCG = (10 × 4) / 500 = 0.08 m to starboard
tan(θ) = 0.08 / 0.60 = 0.133
θ = arctan(0.133) ≈ 7.6° list to starboard
To correct: shift the 10 tons back to the centerline, or move 10 tons an equal distance to port to restore TCG = 0.

9. Adding and Removing Weight

Unlike weight shifts, adding or removing weight changes displacement, draft, and KM (from the hydrostatic tables). It also changes KG. The net effect on GM depends on the height at which the weight is added relative to the vessel's current KM.

Effect on KG When Adding Weight

New KG = (W × KG_old + w × kg) / (W + w)
W = original displacement; KG_old = original KG; w = added weight; kg = height of added weight above keel
Added weight below G: New KG is lower than old KG. GM increases (G moved down toward K, away from M). Stability improves. Example: adding ballast to double-bottom tanks.
Added weight above G: New KG is higher than old KG. GM decreases. Stability worsens. Example: adding deck cargo, fuel to a high day tank, passengers on upper decks.
Added weight at G: New KG equals old KG. But displacement increased, so new KM (from the table) may be slightly different. The effect on GM is minimal.
Removed weight below G: G rises. GM decreases. Stability worsens. Example: consuming fuel from double-bottom tanks during a voyage.
Removed weight above G: G lowers. GM increases. Stability improves. Example: discharging deck cargo, releasing heavy cargo from upper holds.
The Suspended Weight Rule

A weight suspended from a crane or derrick acts as if it were located at the point of suspension (the crane hook or boom tip) — not at the weight's actual position. As soon as a lift is made, G rises to the height of the lifting point. This is why heavy lifts dramatically reduce stability during the lift, even if the final stowage position is low. The exam tests this: "A 20-ton weight is lifted from the deck using the vessel's derrick with a headblock height of 15 m above the keel — where does G act during the lift?" Answer: at the headblock (15 m above keel), regardless of where the weight actually is.

10. Trim, Draft Marks, and Displacement

Trim is the longitudinal inclination of the vessel — the difference between forward and aft drafts. A vessel trimmed by the stern (aft draft greater than forward draft) is the most common and preferred condition for most ships. Trim by the head (forward draft greater) reduces maneuverability and increases slamming in waves.

Reading Draft Marks

Draft marks are painted on the hull at the forward and aft perpendiculars (FP and AP). They show the depth of the keel below the waterline. On US vessels, draft marks are in feet and inches. On metric vessels, marks are in decimeters (tenths of a meter). The bottom of each number is the actual draft at that mark. To read a draft of 12'-6", you would see the number 12 with the waterline above it by 6 inches.

Trim Calculations

Basic Trim Definitions
Trim = AF Draft - FWD Draft (positive = trim by stern)
Mean Draft = (AF Draft + FWD Draft) / 2
Draft at midship ≈ Mean Draft ± hogging/sagging correction
MCT (Moment to Change Trim)

MCT1" = the moment (in foot-tons) required to change trim by 1 inch. MCTC = moment to change trim 1 cm. These values are read from the hydrostatic tables in the stability booklet at the vessel's current displacement.

Change in Trim (inches) = (w × d) / MCT1"
where w = weight added/removed (tons), d = distance from center of flotation F (feet)
Distribution of Trim Change Between FWD and AFT
Change in AF draft = Trim change × (l_F / LBP)
Change in FWD draft = Trim change × (l_A / LBP)
l_F = distance from F to aft draft mark; l_A = distance from F to forward draft mark; LBP = length between perpendiculars
Exam Example — Trim Calculation
Vessel: LBP = 120 m. Current drafts: FWD 4.80 m, AFT 5.20 m. F is 60 m from aft perpendicular. MCT1cm = 25 t·m. Add 50 tons of cargo 20 m forward of F.
Trimming moment = 50 × 20 = 1,000 t·m (forward)
Change in trim = 1,000 / 25 = 40 cm (by head — forward trim increases)
Change in FWD draft = 40 × (60/120) = 20 cm increase
Change in AFT draft = 40 × (60/120) = 20 cm decrease
New FWD draft = 4.80 + 0.20 = 5.00 m
New AFT draft = 5.20 - 0.20 = 5.00 m
The vessel is now on an even keel.

Deadweight vs. Displacement

Displacement (Δ)

Total weight of the vessel including hull, machinery, crew, stores, fuel, ballast, and cargo. Equal to the weight of water displaced. Read from displacement tables using mean draft. Expressed in long tons (2,240 lb), short tons (2,000 lb), or metric tons (1,000 kg).

Deadweight (DWT)

Weight of everything on board except the vessel itself — cargo, fuel, water, stores, crew and effects. DWT = Displacement - Lightship weight. This is the paying cargo capacity. A vessel's DWT determines how much cargo it can carry to its load line.

11. Stability Booklet and Intact Stability Criteria

Every vessel over a certain size must carry an approved Stability Booklet (also called Stability Data Book or Trim and Stability Booklet). This document is prepared by the shipbuilder or naval architect and approved by the flag state or classification society. It provides the data needed to calculate stability for any loading condition.

Contents of the Stability Booklet

General Arrangement and Capacity Plan
Dimensions, tank locations, volumes, LCGs, VCGs of all spaces
Hydrostatic Tables
KM, KB, BM, TPC/TPI, MCT1 cm or inch, LCB, LCF — all as function of draft/displacement
Bonjean Curves
Sectional area curves used for calculating displacement at unusual trims
Cross-Curves of Stability (KN curves)
GZ values at various displacements and heel angles, used to construct GZ curve for any loading condition
Tank Sounding Tables
Volume, weight, LCG, VCG, and FSC (free surface correction) for each tank at each sounding level
Lightship Data
Lightship displacement, KG, LCG — the baseline for all loading calculations
Standard Loading Conditions
Departure and arrival conditions for typical voyages showing that all criteria are met
Grain Loading Information
Maximum permissible grain heeling moments for compliance with grain code (if applicable)
Maximum KG Curves or Tables
Maximum allowable KG (or minimum GM) for each displacement — the master's go/no-go check
Damage Stability Information
Flooding scenarios and residual stability after compartment flooding (for applicable vessels)

IMO Intact Stability Criteria (IS Code 2008)

The International Code on Intact Stability (IS Code 2008) sets minimum stability criteria for vessels in international trade. National administrations (like the USCG) adopt these criteria through domestic regulations (46 CFR Subchapter S for US vessels). The criteria apply to all loading conditions from departure to arrival.

Minimum GM Requirements by Vessel Type
Vessel TypeMinimum GM (corrected for FSC)
General cargo vessels (IS Code)0.15 m
Passenger vessels (subchapter H)Variable — residual GM after damage
Grain carriers (Grain Code)0.30 m (after assumed grain shift)
Sailing vesselsVerified by GZ curve — initial GM not sole criterion
Fishing vessels (Torremolinos)0.35 m
How the Master Uses the Maximum KG Curve

The maximum KG curve (or table) gives the highest allowable KG for each displacement that still meets all stability criteria simultaneously. The master calculates the vessel's actual KG for the proposed loading condition and verifies it is at or below the maximum KG at that displacement. If actual KG exceeds maximum KG, the loading plan must be revised — typically by shifting cargo lower, reducing deck cargo, or adding low ballast. This is the standard pre-departure stability check.

12. Damage Stability Basics

Damage stability refers to the vessel's ability to survive flooding of one or more compartments. SOLAS requires passenger vessels and certain cargo ships to demonstrate damage stability — meaning they remain afloat and upright with positive residual GM after a specified flooding scenario. The USCG exam tests the basic concepts of damage stability rather than complex calculations.

Lost Buoyancy Method

Treats the flooded compartment as open to the sea — the flooded volume is removed from the vessel's buoyancy. The remaining waterplane area and intact compartments must provide enough buoyancy to support the vessel. Used for regulatory damage stability calculations on passenger vessels.

Added Weight Method

Treats flooding as adding the weight of the ingressed water. The vessel sinks deeper and G changes. Simpler to calculate but less accurate at large heel angles. Often used for approximate damage stability assessments and on smaller vessels.

Subdivision and Floodable Length

Vessels are divided into watertight compartments. The floodable length is the maximum length of compartment that can flood without sinking the vessel. A higher subdivision factor (less floodable length per compartment) provides greater damage resistance. Passenger vessels require higher subdivision standards than cargo vessels.

SOLAS Damage Stability Requirements

After flooding, the vessel must: (1) remain afloat with positive freeboard on the intact side; (2) have a residual positive GM; (3) not exceed maximum heel angles; (4) have a range of positive residual GZ of at least 15° beyond the equilibrium heel angle. Passenger ships must survive flooding of any single compartment; larger ships may need to survive two-compartment flooding.

Permeability

Permeability (μ) is the fraction of a compartment volume that can actually be flooded (the rest is occupied by structure, machinery, or cargo). Empty cargo holds: μ = 0.95. Machinery spaces: μ = 0.85. Accommodation spaces: μ = 0.95. Stores: μ = 0.60. A fully flooded empty compartment uses nearly all its volume as added water; a machinery room has 15% of its volume occupied by engines, pumps, and structure.

13. Grain Cargo Stability

Bulk grain is one of the most hazardous cargoes for vessel stability. Unlike liquid in a tank, grain can shift when the vessel rolls — even just a few degrees — causing a permanent heel that can lead to capsize. The International Grain Code (incorporated into SOLAS Chapter VI) governs the carriage of bulk grain worldwide.

Why Grain Is Dangerous

  • Grain is a granular solid that behaves somewhat like a liquid when subject to vibration or motion
  • A full grain hold has a void space at the top (the grain surface is not perfectly flat)
  • When the vessel rolls, grain on the high side can avalanche into the void, shifting the cargo permanently to the low side
  • This is called grain shift — it creates a permanent list similar to a weight shift to the low side
  • Grain shift is not corrected by rolling back — once shifted, the grain stays shifted
  • Grain also settles during a voyage due to vibration, increasing void space and potential shift

International Grain Code — Key Requirements

Document of Authorization: The vessel must carry a Document of Authorization (DOA) issued or approved by the flag state, confirming the vessel is fit to carry bulk grain and that stability data is provided.
Trimming of Grain: Grain must be trimmed (leveled or slightly mounded) to reduce the void volume at the surface. Untrimmed grain has larger assumed heeling moments.
Overstowing and Feeder Ducts: Filled and trimmed holds may be capped with bagged grain or secured surfaces to prevent shift. Feeder ducts allow grain to flow from upper spaces to fill voids below.
Stability Criteria After Assumed Grain Shift:
  • Angle of heel due to grain shift must not exceed 12 degrees
  • Residual GM (after grain shift) must be at least 0.30 meters
  • Net residual area of GZ curve from equilibrium angle to flooding angle must be at least 0.075 m·rad
Grain Heeling Moments: The stability booklet must include grain heeling moment data for each hold at each loading level. These assumed heeling moments are based on the void volume and grain stowage factor. The master uses these to calculate whether the vessel meets the above criteria for the proposed loading plan.
Stowage Factor and Grain Calculations

Stowage factor (SF) is the volume (in cubic feet or cubic meters) occupied by one ton of cargo. For grain: wheat SF ≈ 47–50 ft³/ton; corn SF ≈ 48–52 ft³/ton; soybeans SF ≈ 50–52 ft³/ton. A lower SF means the grain is denser and takes up less volume per ton — fewer voids and less heeling potential. The examiner may ask you to calculate the weight of grain that can be loaded in a hold of known volume:

Weight (tons) = Hold Volume (ft³) / Stowage Factor (ft³/ton)

14. IMDG Code and Hazardous Materials

The International Maritime Dangerous Goods (IMDG) Code governs the transport of hazardous materials by sea. It is mandatory under SOLAS Chapter VII and incorporated into US law through 49 CFR and 46 CFR. The USCG exam tests IMDG Class definitions, segregation requirements, and documentation.

The Nine IMDG Hazard Classes

Class 1
1.1–1.6
Explosives
Hazard: Mass explosion, projection, fire
Exam note: Most restrictive segregation; must be stowed away from all flammable cargoes
Class 2
2.1 Flammable, 2.2 Non-flammable, 2.3 Toxic
Gases
Hazard: Flammability, asphyxiation, toxicity
Exam note: LPG cylinders commonly tested; stow on deck, away from heat
Class 3
Flash point below 60°C
Flammable Liquids
Hazard: Fire and explosion risk
Exam note: Most common on exam; FP cutoff 60°C (140°F); segregate from oxidizers and explosives
Class 4
4.1 / 4.2 / 4.3
Flammable Solids / Spontaneously Combustible / Dangerous When Wet
Hazard: Fire from friction, self-heating, water reaction
Exam note: Class 4.3 (dangerous when wet) produces flammable gas with water — never stow near bilges or wet areas
Class 5
5.1 / 5.2
Oxidizers and Organic Peroxides
Hazard: Intensify fire by releasing oxygen
Exam note: Separate from flammables; organic peroxides need temperature control
Class 6
6.1 / 6.2
Toxic and Infectious Substances
Hazard: Poisoning, disease
Exam note: Segregate from foodstuffs; Class 6.2 requires special containment
Class 7
I / II / III (transport index)
Radioactive Materials
Hazard: Radiation exposure
Exam note: Transport index controls segregation distance; Category III requires 3-meter separation from crew spaces
Class 8
Acids and alkalis
Corrosives
Hazard: Chemical burns, hull and cargo damage
Exam note: Segregate from Class 4.3 and foodstuffs; acids and alkalis must be separated from each other
Class 9
Lithium batteries, dry ice, magnetized material
Miscellaneous Dangerous Goods
Hazard: Varies by substance
Exam note: Lithium batteries frequently tested — many airlines ban them in cargo hold; IMDG Special Provisions apply

IMDG Segregation Requirements

Segregation prevents incompatible dangerous goods from coming into contact in the event of leakage, fire, or explosion. The four segregation categories define the minimum separation required:

"Away from"
Separated by a distance of at least 3 m on deck, or stowed in different ends of the same hold below deck
"Separated from"
In different compartments or holds; on deck, separated by a full compartment or hold when the other cargo is below deck
"Separated by a complete compartment or hold from"
On deck or below deck, separated either athwartship or fore-and-aft by a complete compartment or hold
"Separated longitudinally by an intervening complete compartment or hold from"
Most restrictive — no cargo in the same or adjacent hold, and the separation must be fore-and-aft, not just athwartship

IMDG Documentation Requirements

Dangerous Goods Declaration (DGD): Prepared by the shipper for each consignment of dangerous goods. Must include: proper shipping name, UN number, hazard class and division, packing group (I/II/III), total quantity, number and type of packages, and shipper's certification. The master must not accept dangerous goods without this document.
Cargo Manifest / Dangerous Goods Manifest: A consolidated list of all dangerous goods on board, including their stowage locations. Must be kept on board during the voyage and made available to port state control officers on request.
Emergency Response Information: The IMDG Code Emergency Schedules (EmS) and the Medical First Aid Guide (MFAG) must be on board. These provide fire-fighting measures and first aid instructions specific to each hazard class.
Packing Certificate: For FCL (full container load) containers, the party responsible for packing must provide a Container/Vehicle Packing Certificate confirming the container has been properly packed, secured, and the dangerous goods properly identified and documented.

15. Cargo Securing — Lashing, Blocking, and Bracing

Cargo securing prevents cargo from shifting during the voyage. Shifted cargo raises the center of gravity, creates list, and in extreme cases causes capsize. The USCG exam tests the principles of cargo securing, the Cargo Securing Manual requirements, and lashing calculations.

Methods of Cargo Securing

Lashing

Wire rope, chain, or webbing straps attached from the cargo to deck lashing points (pad eyes, sockets). Lashings restrain the cargo from sliding, tipping, or lifting. Safe Working Load (SWL) must exceed the forces calculated from ship motion.

Blocking and Bracing

Wooden blocks, beams, or proprietary frames wedged between cargo units and ship structures to prevent movement. Particularly effective for preventing sliding. Must be secured so they cannot become projectiles if cargo shifts.

Dunnage

Packing material (wood boards, mats, air bags) placed between cargo units and the ship's structure to: distribute weight evenly, prevent damage from contact, allow air circulation, and protect cargo from sweat and moisture.

Container Securing Hardware

Twist Locks
Lock containers to cell guides or to each other; standard for stacking at corners
Bridge Fittings
Connect adjacent containers athwartship; also called cross lashings at top corners
Lashing Rods
Turnbuckle-equipped rods from container corners to deck sockets; direct lashings
Stacking Cones
Intermediate fittings between stacked containers providing lateral and vertical restraint

Forces Acting on Cargo

The CSS Code (Code of Safe Practice for Cargo Stowage and Securing) provides methods to calculate the forces on cargo from ship motion. The accelerations depend on the ship's length, beam, block coefficient, metacentric height, and service area. The three primary forces are:

Longitudinal forces (fore-and-aft): From pitching and heaving. Typically 0.3g to 0.5g for open ocean passages. Cargo can slide forward or aft under these forces.
Transverse forces (side to side): From rolling. Can reach 0.5g to 0.8g in severe weather. Most dangerous for cargo shift because the transverse acceleration is highest at the deck edges and decreases toward the centerline.
Vertical forces (up-down): From heaving. Typically reduce the effective weight of cargo (cargo feels lighter due to upward acceleration). A stiff vessel's rapid roll produces high vertical accelerations — this is a reason stiff vessels are hard on cargo lashings.
Cargo Securing Manual (CSM) Requirements

SOLAS VI/5.6 requires all vessels of 500 GT and above built after January 1, 1998 to carry an approved Cargo Securing Manual. The CSM must contain: inventory of all portable securing equipment (with SWL); location of fixed deck fittings and their SWL; securing arrangements for all types of cargo units the vessel regularly carries; instructions for maintaining and inspecting securing equipment. The CSM must be specific to the vessel — generic manuals are not acceptable. USCG Port State Control examiners inspect the CSM during vessel examinations.

16. Deck Cargo Rules

Deck cargo presents unique stability risks because it is loaded high in the vessel, raising G and reducing GM. Special rules and precautions apply to vessels carrying cargo on open decks.

Timber Deck Cargo

Timber (lumber) carried on deck entitles the vessel to a reduced freeboard (timber load line) because the timber provides reserve buoyancy and reduces the risk of progressive flooding. However, timber also absorbs water during the voyage, increasing its weight and raising G. Stability calculations for timber vessels must account for water absorption (typically 10–15% weight increase). The Timber Load Line Convention and ILLC protocols apply. Timber must be secured with lashings rated for the expected sea conditions.

Container Stacking on Deck

Containers on deck must be secured with twist locks, bridge fittings, and lashing rods per the CSM. Stack weights are limited by the structural capacity of the deck, the container corner post design load, and the stability requirements. High stacks of heavy containers dramatically raise G. Container vessels use ballast to compensate when stacking heavy containers high on deck.

Icing on Deck Cargo

Ice accumulation on deck cargo, rigging, and superstructure raises G and reduces freeboard. High-latitude and cold-weather routes require icing allowances in the stability calculation. The IS Code provides icing allowances: 30 kg/m² on exposed weather decks and 7.5 kg/m² on projected lateral area of the vessel above the waterline. Vessels in icing conditions must be prepared to remove ice and recheck stability. Icing has capsized numerous fishing vessels and smaller cargo ships.

Wind Heeling Moment

The IS Code criteria include a weather criterion: the vessel must withstand the combined effect of beam wind pressure on the exposed lateral area plus rolling. The wind heeling lever (lw1) from a 26 m/s (50-knot) wind must be less than 0.5 × GZ at the static angle of heel due to that wind, with an area reserve requirement. This criterion is most demanding for vessels with large above-deck structures — ferries, ro-ro vessels, and container ships with high deck cargo.

Freeboard and Load Lines

The Load Line Convention (ICLL 1966) sets minimum freeboard requirements — the distance from the waterline to the freeboard deck. Load line marks on the hull show the maximum draft in various conditions: S (Summer), W (Winter), WNA (Winter North Atlantic), T (Tropical), F (Fresh Water), TF (Tropical Fresh Water). Loading beyond the applicable load line mark is a serious violation (46 CFR 42). Deck cargo that would submerge the load line mark is prohibited. The USCG exam tests the locations of load line marks and which mark applies in which zone and season.

17. Cargo Manifest and Documentation

Cargo documentation establishes what is on board, where it is stowed, and who is responsible. Proper documentation is required by USCG regulations, customs law, and international conventions. Missing or incorrect cargo documentation is a common PSC deficiency and exam topic.

Cargo Manifest
Purpose: Complete list of all cargo on board: description, quantity, shipper, consignee, port of loading, port of discharge, bill of lading number.
Regulatory note: Required by 19 CFR (US Customs) for all arriving and departing vessels. Must be filed electronically via CBP's Automated Manifest System (AMS) 24 hours before loading at foreign ports.
Bill of Lading (B/L)
Purpose: Contract of carriage between shipper and carrier. Serves as: (1) receipt for cargo, (2) evidence of contract of carriage, (3) document of title.
Regulatory note: Issued by carrier for each shipment. The master signs the B/L; the master can add clauses (e.g., 'apparent good order') noting any visible damage. A clean B/L means cargo was received in apparent good condition.
Stowage Plan
Purpose: Diagram showing the location of each cargo parcel in the vessel — which hold, which tier, which bay (for container ships). Used by port terminals, stevedores, and the master.
Regulatory note: Required for dangerous goods (must show DG locations). For container vessels, a computerized Bay Plan serves this function. The master must verify the stowage plan before departure.
Dangerous Goods Manifest
Purpose: Separate listing of all dangerous goods on board with UN number, class, quantity, and stowage location. A subset of the cargo manifest focusing on IMDG-regulated goods.
Regulatory note: Required by SOLAS VII/4 for all vessels carrying packaged dangerous goods. Must be kept on board and presented to port state control on demand. A copy must be available ashore.
Mate's Receipt
Purpose: Acknowledgment signed by the chief mate confirming receipt of cargo and its apparent condition at the time of loading. Basis for issuing the Bill of Lading.
Regulatory note: Used between the terminal and the vessel. If the mate notes damage or discrepancy, the receipt is claused — this becomes the basis for claims against the shipper or terminal.
Notice of Readiness (NOR)
Purpose: Written notice from the master to the charterer stating that the vessel has arrived at the port and is ready to load or discharge cargo. Starts the laytime clock for demurrage calculations.
Regulatory note: Required under voyage charter parties. Timing of NOR affects whether the shipowner receives additional payment (demurrage) for delays. The master must understand the charter party terms before tendering NOR.

Cargo Calculations — Loading Table Example

KG Calculation Table
ItemWeight (t)KG (m)Moment (t·m)
Lightship1,2004.805,760
Hold 1 cargo (lower)3002.10630
Hold 2 cargo (lower)2502.30575
Hold 3 cargo (upper)1506.801,020
Deck cargo809.20736
Fuel (double bottom)1200.8096
Freshwater401.2048
Stores and crew205.00100
TOTAL2,1608,965
KG = Total Moment / Total Weight = 8,965 / 2,160 = 4.15 m
From hydrostatic tables at 2,160 t displacement: KM = 4.55 m. GM (solid) = 4.55 - 4.15 = 0.40 m. After FSC of 0.08 m: GM (corrected) = 0.32 m. Vessel meets minimum criteria.

18. Frequently Asked Questions

What is metacentric height (GM) and how does it affect vessel stability?

Metacentric height (GM) is the vertical distance from the center of gravity (G) to the metacenter (M). A positive GM means M is above G and the vessel is stable — it will return to upright after heeling. A negative GM means G is above M and the vessel is unstable. The exam formula is GM = KB + BM - KG. A large positive GM produces a stiff vessel with a short, snappy roll; a small positive GM produces a tender vessel with a slow, sluggish roll. Both extremes create problems: stiff vessels are uncomfortable and place stress on cargo and structures; tender vessels may not meet minimum stability criteria.

What is the difference between list and angle of loll?

List is a permanent heel to one side caused by an off-center transverse center of gravity (TCG). The vessel has positive GM but heels because G is not on the centerline. Correction: shift weight back to centerline. Angle of loll is caused by negative GM — the vessel's G is above M. The vessel heels to one side (or both sides alternately) and rests at an angle where the righting arm GZ equals zero. This is far more dangerous than list. The WRONG correction for loll is to move weight to the high side — this can cause catastrophic capsize. The correct action is to lower G: add low ballast, flood double-bottom tanks, or remove high weights.

How do you calculate free surface correction (FSC)?

Free surface correction (FSC) accounts for the virtual rise in G caused by liquid sloshing in partially filled tanks. Formula: FSC = (i x density of tank liquid) / (V x density of seawater), where i is the second moment of area (moment of inertia) of the free surface about its own centroid, and V is the vessel displacement volume. In practice, FSC values come from the stability booklet for each tank at each sounding level. The corrected GM = GM (solid) - FSC. Free surface effect is worst in wide tanks, least in narrow tanks. Longitudinal subdivisions dramatically reduce FSC because i is proportional to the cube of tank width.

What is the angle of vanishing stability (AVS) and why does it matter?

The angle of vanishing stability (AVS) is the angle of heel at which the GZ righting arm curve crosses zero on the way back down — meaning the vessel has no more righting moment and will capsize if heeled further. A vessel with a large AVS has a wide range of positive stability and is much safer in heavy weather. IMO intact stability criteria require that the range of positive stability extend to at least 30 degrees beyond the angle of maximum GZ. Vessels with AVS below 90 degrees are considered to have limited range of stability. The exam tests your ability to read a GZ curve and identify: the angle of maximum GZ, the area under the curve (dynamic stability), and the AVS.

How does adding or removing weight affect trim?

Trim is the difference between forward draft and aft draft. Adding weight forward of the center of flotation (F) trims the vessel by the head (bow goes down). Adding weight aft of F trims by the stern. The moment to change trim one inch (MCT1" or MCTC in metric) from the stability booklet gives the trim lever. Formula: Change in trim = (weight x distance from F) / MCTC. To calculate individual draft changes: forward draft change = (change in trim x distance from F to forward draft mark) / LBP. Draft marks are read at the forward and aft perpendiculars; the mean draft gives displacement from the hydrostatic tables.

What are the IMDG Code segregation categories for dangerous goods?

The IMDG Code has four segregation categories: (1) Away from — minimum horizontal or vertical separation; (2) Separated from — different compartments or holds, or on deck separated by a full compartment/hold below deck; (3) Separated by a complete compartment or hold from — athwartship or fore-and-aft by a full compartment; (4) Separated longitudinally by an intervening complete compartment or hold from — the most restrictive, requiring full longitudinal separation. The exam tests which class combinations require which segregation level. Explosives (Class 1) require the most restrictive segregation from flammable liquids (Class 3), oxidizers (Class 5.1), and corrosives (Class 8).

What grain stability requirements apply to vessels carrying bulk grain?

Vessels carrying bulk grain must comply with the International Grain Code (SOLAS Chapter VI and Resolution MSC.23(59)). Key requirements: the vessel must have a Document of Authorization for the carriage of grain; the master must have stability data including the assumed grain heeling moments; after loading, the angle of heel due to grain shift must not exceed 12 degrees; the net residual area of the GZ curve between the heel angle and the flooding angle must not be less than 0.075 meter-radians; and the GM must not be less than 0.30 meters. Untrimmed grain (grain not leveled) has higher assumed heeling moments than trimmed grain. These requirements appear on USCG Master exam questions about grain cargo.

What must a cargo securing manual contain?

A Cargo Securing Manual (CSM), required by SOLAS VI/5.6 for vessels of 500 GT and above, must contain: a description of the fixed lashing points, sockets, and container fittings on deck; specifications for all portable securing equipment (lashings, chains, turnbuckles, shackles, twist locks) including safe working loads (SWL); securing arrangements for standard cargo units, containers, and vehicles; guidance on cargo stowage and securing for different sea conditions; and instructions for maintaining and inspecting securing gear. The CSM must be approved by the flag state or a recognized classification society. The USCG exam tests the master's obligation to ensure cargo is secured before departure.

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